Subgroups — Dic₁₇×#92788 #46828186

Order 34476.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#92788	C₂	1	1	yes	maximal, characteristic
2	C₁₃²×Dic₁₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×#92788	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃²×C₁₇	C₂×C₃	1	1	yes	characteristic
5	C₁₃²×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₁₃⋊C₃×Dic₁₇	—	13	14	no	maximal
7	C₄×#92788	—	17	1	no	maximal, Hall
8	C₂×C₁₇×C₁₃⋊C₃	—	13	14	no	—
9	C₂×#92788	D₁₇	1	1	yes	characteristic
10	C₁₃×Dic₁₇	C₁₃⋊C₃	1	14	yes	complemented
11	C₄×C₁₃²	—	17	1	no	Hall
12	C₁₇×C₁₃⋊C₃	—	13	14	no	—
13	#92788	Dic₁₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₁₃×C₁₇	C₂×C₁₃⋊C₃	1	14	yes	—
15	C₂×C₁₃²	C₃×D₁₇	1	1	yes	characteristic
16	C₁₃×C₁₇	C₄×C₁₃⋊C₃	1	14	yes	complemented
17	C₃×Dic₁₇	—	169	1	no	Hall
18	C₁₃²	C₃×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
19	C₄×C₁₃⋊C₃	—	221	14	no	—
20	C₂×C₃×C₁₇	—	169	1	no	—
21	C₂×C₁₃⋊C₃	—	13	14	no	—
22	Dic₁₇	#92788	1	1	yes	characteristic, direct product factor, Hall
23	C₄×C₁₃	—	17	14	no	—
24	C₃×C₁₇	—	169	1	no	Hall
25	C₁₃⋊C₃	—	13	14	no	—
26	C₂×C₁₇	C₂×#92788	1	1	yes	characteristic
27	C₂×C₁₃	D₁₇×C₁₃⋊C₃	1	14	yes	—
28	C₁₇	C₄×#92788	1	1	yes	characteristic, complemented, Sylow
29	C₁₃	C₁₃⋊C₃×Dic₁₇	1	14	yes	complemented
30	C₃×C₄	—	2873	1	no	Hall
31	C₂×C₃	—	169	1	no	—
32	C₄	—	17	1	no	Sylow
33	C₃	—	169	1	no	Sylow
34	C₂	D₁₇×#92788	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₇×#92788
commutator, hypocenter	C₁₃²×C₁₇	C₃×C₄
Fitting, socle, cosocle	C₂×C₁₃²×C₁₇	C₂×C₃
prime radical	C₂×C₁₇×#92788	C₂
LCS	G ▷ C₁₃²×C₁₇
UCS	C₁ ◁ C₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₃²×Dic₁₇	C₃	semidirect
3. C₁₇×#92788	C₄	semidirect
5. C₁₃²×C₁₇	C₃×C₄	semidirect
10. C₁₃×Dic₁₇	C₁₃⋊C₃	semidirect
13. #92788	Dic₁₇	direct (N × H)
16. C₁₃×C₁₇	C₄×C₁₃⋊C₃	semidirect
18. C₁₃²	C₃×Dic₁₇	semidirect
22. Dic₁₇	#92788	direct (N × H)
28. C₁₇	C₄×#92788	semidirect
29. C₁₃	C₁₃⋊C₃×Dic₁₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₇×#92788	2
C₁₃²×Dic₁₇	3
C₁₃⋊C₃×Dic₁₇	13
C₄×#92788	17

Subgroups — Dic17×#92788 #46828186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₇×#92788 #46828186